Back to Make geometric constructions — Problem 3 · Task Set 12

Exercises: Make Formal Geometric Constructions

Work through each section in order. For construction problems, show all compass arcs and straightedge marks — do not erase construction lines. For multiple-choice problems, choose the best answer.

Grade 9·22 problems·~35 min·Common Core Math - HS Geometry·standard·hsg-co-d-12

Work through problems with immediate feedback

Fluency Practice

Each problem tests your knowledge of the six standard constructions. Identify the correct step, tool use, or construction outcome.

Valentina is bisecting segment AB. She draws arcs from A and B using a compass set to a radius equal to exactly half the length of AB. Will her construction work?

Yes — setting the radius to exactly half ensures the arcs meet at the midpoint.

No — setting the radius to exactly half means the arcs only just touch at the midpoint and do not produce two distinct intersection points needed to draw the bisector.

No — the radius must be set to exactly the full length of AB for the construction to work.

Yes — the compass radius does not affect where the arcs intersect, so any setting works.